Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of contents

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[151.] Fournier in Hydrographia 1. 12. C. 35.
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[152.] Didericus Rembrantz a Nierop in Animadverſionibus de inveniendis longitudinibus.
Page: 299
[153.] BREVIS INSTRUCTIO DE USU HOROLO-GIORUM AD INVENIENDAS LONGITUDINES. I.
Page: 300
[154.] II.
Page: 300
[155.] III.
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[156.] IV.
Page: 300
[157.] V. Reducere horologia ad rectam dierum menſuram vel cogno-ſcere quanto citius vel tardius ſpatio 24 horarum movean-tur.
Page: 301 (196)
[158.] VI. Ope Horologiorum mari invenire longitudinem loci in quo verſaris.
Page: 307 (202)
[159.] VII. Mari invenire horam diei.
Page: 309 (204)
[160.] VIII. Quomodo ex obſervatione ortus & occaſus Solis & ex hora horologiorum longitudo mari inveniri queat.
Page: 310 (205)
[161.] IX.
Page: 314 (209)
[162.] X.
Page: 314 (209)
[163.] XI.
Page: 315 (210)
[164.] XII.
Page: 315 (210)
[165.] FINIS.
Page: 316 (211)
[166.] EXCERPTA EX LITERIS DATIS LONDINI {13/23} JANUARII MDCLXV.
Page: 316 (211)
[167.] EXCERPTA EX LITERIS HAGÆ CO-MITUM, DIE XXVI. FEBRUAR MDCLXV. DATIS.
Page: 318 (213)
[168.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA.
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[169.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA. I. Obſervationes Abbatis Catelani in propoſitio-nem, quæ fundamentum eſt 4æ. partis tra-ctatus de Pendulis, Hugenii.
Page: 322
[170.] II. Domini Abbatis Catelani Examen Ma-thematicum Centri Oſcillationis.
Page: 324 (219)
[171.] MONITUM.
Page: 327 (222)
[172.] III. Excerpta ex literis Domini Hugenii, quibus re-ſpondet obſervationi Abbatis Catelani in 4am. pro-poſitionem Tractatus de centris Oſcillationis.
Page: 327 (222)
[173.] IV. Exceptio Abbatis Catelani ad reſponſionem Hugenii.
Page: 330 (225)
[174.] V. Objectio Abbatis Catelani contra motum Pendulorum in Cycloidibus.
Page: 332 (227)
[175.] VI. Reſponſio ad objectiones Hugenii adverſus me-thodum Abbatis Catelani de determinan-do Centro Oſcillationis.
Page: 333 (228)
[176.] VII. Excerpta ex litteris D. Bernoullii datis Baſileæ ad Autorem Diarii Pariſienſis, de Controverſia, inter Abbatem Catelanum & Hugenium, de Centro Oſcillationis.
Page: 335 (230)
[177.] VIII. Excerpta ex literis Dni. Hugenii ad Auctores Diarii Pariſienſis, datis Hagæ 8. Funii 1684. quæ continent ejus reſponſionem ad exceptio-nem Dni. Abbatis Catelani, de cen-tro Oſcillationis.
Page: 337 (232)
[178.] IX. Reſponſio Dni. Abbatis Catelani ad literas Dni. Bernoulli de Controverſia ſua cum Dno. Hu-genio de centro Oſcillationis .
Page: 340 (235)
[179.] X. Dn. Bernouillii narratio controverſiæ inter Dn. Hugenium & Abbatem Catelanum agitatæ de Centro Oſcillationis, quæ loco Anim-adverſionis eſſe poterit in Reſpon-ſionem Dn. Catelani. Excerpta ex Litteris Dn. Bernoullii Lipſiam miſſis.
Page: 342 (237)
[180.] XI. Litteræ Dni Marchionis de l’Hôpital ad Dum Huge-nium, in quibus contendit, ſeregulam hujus Au-ctoris de Centro oſcillationis penduli compoſiti demonſtrare per cauſam Phyſicam, & re-ſpondere ſimul Dno Bernoulli.
Page: 347 (242)
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              <pb o="94" file="0140" n="151" rhead="CHRISTIANI HUGENII"/>
            cum K E ſit breviſſima omnium quæ cadunt inter parallelas
              <lb/>
              <note position="left" xlink:label="note-0140-01" xlink:href="note-0140-01a" xml:space="preserve">
                <emph style="sc">De linea</emph>
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                <emph style="sc">RUM CUR-</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO</emph>
                <lb/>
                <emph style="sc">NE</emph>
              .</note>
            E L, K M, erit ea minor quam M L, ac proinde minor
              <lb/>
            quoque omnino quam M D. </s>
            <s xml:id="echoid-s2082" xml:space="preserve">Eodem modo & </s>
            <s xml:id="echoid-s2083" xml:space="preserve">H D minor
              <lb/>
            oſtendetur quam N C, & </s>
            <s xml:id="echoid-s2084" xml:space="preserve">G C minor quam O B, & </s>
            <s xml:id="echoid-s2085" xml:space="preserve">F B
              <lb/>
            minor quam P A. </s>
            <s xml:id="echoid-s2086" xml:space="preserve">Cum ſit ergo P A major quam F B, erunt
              <lb/>
            duæ ſimul P A, O F majores quam O B. </s>
            <s xml:id="echoid-s2087" xml:space="preserve">Item quum O B
              <lb/>
            ſit major quam G C, erunt duæ ſimul O B, N G, majo-
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            res quam N C. </s>
            <s xml:id="echoid-s2088" xml:space="preserve">Sed duæ P A, O F majores erant quam O B.
              <lb/>
            </s>
            <s xml:id="echoid-s2089" xml:space="preserve">Itaque tres ſimul P A, O F, N G omnino majores erunt
              <lb/>
            quam N C. </s>
            <s xml:id="echoid-s2090" xml:space="preserve">Rurſus, quia N C major quam H D, erunt duæ
              <lb/>
            ſimul N C, M H majores quam M D. </s>
            <s xml:id="echoid-s2091" xml:space="preserve">Unde, ſi loco N C
              <lb/>
            ſumantur tres hæ ipſa majores P A, O F, N G, erunt omni-
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            no hæ quatuor P A, O F, N G, M H majores quam M D: </s>
            <s xml:id="echoid-s2092" xml:space="preserve">
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            ac proinde eædem quoque omnino majores recta K E, quia
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            ipſa M D major erat quam K E. </s>
            <s xml:id="echoid-s2093" xml:space="preserve">Diximus autem ſubtenſas
              <lb/>
            omnes A F, F G, G H, H K majorem rationem habere ad
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            omnes perpendiculares P A, O F, N G, M H, quam linea
              <lb/>
            Q ad K E. </s>
            <s xml:id="echoid-s2094" xml:space="preserve">Ergo cum dictis perpendicularibus minor etiam
              <lb/>
            ſit K E, habebunt dictæ ſubtenſæ ad K E omnino majorem
              <lb/>
            rationem quam Q ad K E. </s>
            <s xml:id="echoid-s2095" xml:space="preserve">Ergo ſubtenſæ ſimul ſumptæ
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            majores erunt rectâ Q. </s>
            <s xml:id="echoid-s2096" xml:space="preserve">Hæc autem ipſa curvâ A G K major
              <lb/>
            ſumpta fuit. </s>
            <s xml:id="echoid-s2097" xml:space="preserve">Ergo ſubtenſæ A F, F G, G H, H K ſimul
              <lb/>
            majores erunt curva A G K cujus partibus ſubtenduntur; </s>
            <s xml:id="echoid-s2098" xml:space="preserve">
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            quod eſt abſurdum, cum ſingulæ ſuis arcubus ſint minores. </s>
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              <lb/>
            Non igitur poterunt eſſe duæ curvæ lineæ quæ quemadmo-
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            dum dictum fuit ſeſe habeant. </s>
            <s xml:id="echoid-s2100" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s2101" xml:space="preserve"/>
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          <head xml:id="echoid-head83" xml:space="preserve">PROPOSITIO IV.</head>
          <p style="it">
            <s xml:id="echoid-s2102" xml:space="preserve">SI ab eodem puncto duæ lineæ exeant in partem
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            unam inflexæ, & </s>
            <s xml:id="echoid-s2103" xml:space="preserve">in eandem partem cavæ, ita
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            vero mutuo comparatæ ut rectæ omnes, quæ alte-
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            ram earum contingunt, alteri occurrant ad angu-
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            los rectos; </s>
            <s xml:id="echoid-s2104" xml:space="preserve">poſterior hæc prioris evolutione, à pun-
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            cto communi cœpta, deſcribetur.</s>
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